Auction-based cooperation mechanism to parts scheduling for flexible job shop with inter-cells

This paper addresses cell part scheduling (CPS) problem. In this problem, parts may need to visit machines in different cells with consideration Inter-cell transportation time. The processing route of parts can be flexible. The objective is to minimize the overall process make-span. An integer nonlinear programming (INLP) model is formulated to determine the schedule scheme of all parts. An auction-based heuristic approach is proposed to solve it, which focuses on dealing with cooperation between different cells. In this approach, each cell can act as an auctioneer or a bidder. In an auction, it contains call for auction, bid construction, modify bids and winner announcement. A reference matrix is also applied in the auction to guarantee parts to finish as early as possible. Numerical experiments were conducted to test the auction-based approach. The results demonstrate the effectiveness, sensitivity and stability of the proposed auction-based approach, especially suitable for instances in large scale within a short calculating time.